Well, this is a head scratcher… the Customizer just started working. No changes were done.
I was trying to edit the Widget Pack using the WP plugin editor to comment out the code which registered the Connections Shortcode Widgets sidebar so it would not run. I was not able to make the edit because it seems your web host blocks loopback requests which is required for the WP plugin editor to work. You should contact them about that. If they refuse to enable loopback requests, you might want to seek a more WP friendly host.
Anyway, right after that edit failed to apply, it just started working. There’s no reason I can think of why it would just start working. You see, something can be rare and unique… or perhaps you or someone else made changes while I was debugging???
At the very least I know know there is some condition which exists with the Widget Pack which could cause the Customizer to fail to load. Please let me know when and if it happens again.